How can I create a texture that looks like a woven strands of metal?
I would try doing this with a procedural texture on a torus.

Using a simple voronoi texture and scaling it so that it creates a texture for the vertical strands. And feeding that to control the mix between a transparent and glossy shader.



Then use the same kind of setup but rotated 90 degrees for the horizontal strands.



Then mix the two textures (with a multiply operation), and use the resulting image to control the mix between glossy and transparent, but also use that to create some displacement. Adding a Brightness/Contrast node will give you control for the transparency and the amount of displacement.